lib/prio_tree.c

   1 /*
   2  * lib/prio_tree.c - priority search tree
   3  *
   4  * Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh@umich.edu>
   5  *
   6  * This file is released under the GPL v2.
   7  *
   8  * Based on the radix priority search tree proposed by Edward M. McCreight
   9  * SIAM Journal of Computing, vol. 14, no.2, pages 257-276, May 1985
  10  *
  11  * 02Feb2004    Initial version
  12  */
  13
  14 #include <linux/init.h>
  15 #include <linux/mm.h>
  16 #include <linux/prio_tree.h>
  17
  18 /*
  19  * A clever mix of heap and radix trees forms a radix priority search tree (PST)
  20  * which is useful for storing intervals, e.g, we can consider a vma as a closed
  21  * interval of file pages [offset_begin, offset_end], and store all vmas that
  22  * map a file in a PST. Then, using the PST, we can answer a stabbing query,
  23  * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
  24  * given input interval X (a set of consecutive file pages), in "O(log n + m)"
  25  * time where 'log n' is the height of the PST, and 'm' is the number of stored
  26  * intervals (vmas) that overlap (map) with the input interval X (the set of
  27  * consecutive file pages).
  28  *
  29  * In our implementation, we store closed intervals of the form [radix_index,
  30  * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
  31  * is designed for storing intervals with unique radix indices, i.e., each
  32  * interval have different radix_index. However, this limitation can be easily
  33  * overcome by using the size, i.e., heap_index - radix_index, as part of the
  34  * index, so we index the tree using [(radix_index,size), heap_index].
  35  *
  36  * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
  37  * machine, the maximum height of a PST can be 64. We can use a balanced version
  38  * of the priority search tree to optimize the tree height, but the balanced
  39  * tree proposed by McCreight is too complex and memory-hungry for our purpose.
  40  */
  41
  42 /*
  43  * The following macros are used for implementing prio_tree for i_mmap
  44  */
  45
  46 #define RADIX_INDEX(vma)  ((vma)->vm_pgoff)
  47 #define VMA_SIZE(vma)     (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
  48 /* avoid overflow */
  49 #define HEAP_INDEX(vma)   ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))
  50
  51
  52 static void get_index(const struct prio_tree_root *root,
  53     const struct prio_tree_node *node,
  54     unsigned long *radix, unsigned long *heap)
  55 {
  56         if (root->raw) {
  57                 struct vm_area_struct *vma = prio_tree_entry(
  58                     node, struct vm_area_struct, shared.prio_tree_node);
  59
  60                 *radix = RADIX_INDEX(vma);
  61                 *heap = HEAP_INDEX(vma);
  62         }
  63         else {
  64                 *radix = node->start;
  65                 *heap = node->last;
  66         }
  67 }
  68
  69 static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
  70
  71 void __init prio_tree_init(void)
  72 {
  73         unsigned int i;
  74
  75         for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
  76                 index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
  77         index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
  78 }
  79
  80 /*
  81  * Maximum heap_index that can be stored in a PST with index_bits bits
  82  */
  83 static inline unsigned long prio_tree_maxindex(unsigned int bits)
  84 {
  85         return index_bits_to_maxindex[bits - 1];
  86 }
  87
  88 static void prio_set_parent(struct prio_tree_node *parent,
  89                             struct prio_tree_node *child, bool left)
  90 {
  91         if (left)
  92                 parent->left = child;
  93         else
  94                 parent->right = child;
  95
  96         child->parent = parent;
  97 }
  98
  99 /*
 100  * Extend a priority search tree so that it can store a node with heap_index
 101  * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
 102  * However, this function is used rarely and the common case performance is
 103  * not bad.
 104  */
 105 static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
 106                 struct prio_tree_node *node, unsigned long max_heap_index)
 107 {
 108         struct prio_tree_node *prev;
 109
 110         if (max_heap_index > prio_tree_maxindex(root->index_bits))
 111                 root->index_bits++;
 112
 113         prev = node;
 114         INIT_PRIO_TREE_NODE(node);
 115
 116         while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
 117                 struct prio_tree_node *tmp = root->prio_tree_node;
 118
 119                 root->index_bits++;
 120
 121                 if (prio_tree_empty(root))
 122                         continue;
 123
 124                 prio_tree_remove(root, root->prio_tree_node);
 125                 INIT_PRIO_TREE_NODE(tmp);
 126
 127                 prio_set_parent(prev, tmp, true);
 128                 prev = tmp;
 129         }
 130
 131         if (!prio_tree_empty(root))
 132                 prio_set_parent(prev, root->prio_tree_node, true);
 133
 134         root->prio_tree_node = node;
 135         return node;
 136 }
 137
 138 /*
 139  * Replace a prio_tree_node with a new node and return the old node
 140  */
 141 struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
 142                 struct prio_tree_node *old, struct prio_tree_node *node)
 143 {
 144         INIT_PRIO_TREE_NODE(node);
 145
 146         if (prio_tree_root(old)) {
 147                 BUG_ON(root->prio_tree_node != old);
 148                 /*
 149                  * We can reduce root->index_bits here. However, it is complex
 150                  * and does not help much to improve performance (IMO).
 151                  */
 152                 root->prio_tree_node = node;
 153         } else
 154                 prio_set_parent(old->parent, node, old->parent->left == old);
 155
 156         if (!prio_tree_left_empty(old))
 157                 prio_set_parent(node, old->left, true);
 158
 159         if (!prio_tree_right_empty(old))
 160                 prio_set_parent(node, old->right, false);
 161
 162         return old;
 163 }
 164
 165 /*
 166  * Insert a prio_tree_node @node into a radix priority search tree @root. The
 167  * algorithm typically takes O(log n) time where 'log n' is the number of bits
 168  * required to represent the maximum heap_index. In the worst case, the algo
 169  * can take O((log n)^2) - check prio_tree_expand.
 170  *
 171  * If a prior node with same radix_index and heap_index is already found in
 172  * the tree, then returns the address of the prior node. Otherwise, inserts
 173  * @node into the tree and returns @node.
 174  */
 175 struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
 176                 struct prio_tree_node *node)
 177 {
 178         struct prio_tree_node *cur, *res = node;
 179         unsigned long radix_index, heap_index;
 180         unsigned long r_index, h_index, index, mask;
 181         int size_flag = 0;
 182
 183         get_index(root, node, &radix_index, &heap_index);
 184
 185         if (prio_tree_empty(root) ||
 186                         heap_index > prio_tree_maxindex(root->index_bits))
 187                 return prio_tree_expand(root, node, heap_index);
 188
 189         cur = root->prio_tree_node;
 190         mask = 1UL << (root->index_bits - 1);
 191
 192         while (mask) {
 193                 get_index(root, cur, &r_index, &h_index);
 194
 195                 if (r_index == radix_index && h_index == heap_index)
 196                         return cur;
 197
 198                 if (h_index < heap_index ||
 199                     (h_index == heap_index && r_index > radix_index)) {
 200                         struct prio_tree_node *tmp = node;
 201                         node = prio_tree_replace(root, cur, node);
 202                         cur = tmp;
 203                         /* swap indices */
 204                         index = r_index;
 205                         r_index = radix_index;
 206                         radix_index = index;
 207                         index = h_index;
 208                         h_index = heap_index;
 209                         heap_index = index;
 210                 }
 211
 212                 if (size_flag)
 213                         index = heap_index - radix_index;
 214                 else
 215                         index = radix_index;
 216
 217                 if (index & mask) {
 218                         if (prio_tree_right_empty(cur)) {
 219                                 INIT_PRIO_TREE_NODE(node);
 220                                 prio_set_parent(cur, node, false);
 221                                 return res;
 222                         } else
 223                                 cur = cur->right;
 224                 } else {
 225                         if (prio_tree_left_empty(cur)) {
 226                                 INIT_PRIO_TREE_NODE(node);
 227                                 prio_set_parent(cur, node, true);
 228                                 return res;
 229                         } else
 230                                 cur = cur->left;
 231                 }
 232
 233                 mask >>= 1;
 234
 235                 if (!mask) {
 236                         mask = 1UL << (BITS_PER_LONG - 1);
 237                         size_flag = 1;
 238                 }
 239         }
 240         /* Should not reach here */
 241         BUG();
 242         return NULL;
 243 }
 244
 245 /*
 246  * Remove a prio_tree_node @node from a radix priority search tree @root. The
 247  * algorithm takes O(log n) time where 'log n' is the number of bits required
 248  * to represent the maximum heap_index.
 249  */
 250 void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
 251 {
 252         struct prio_tree_node *cur;
 253         unsigned long r_index, h_index_right, h_index_left;
 254
 255         cur = node;
 256
 257         while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
 258                 if (!prio_tree_left_empty(cur))
 259                         get_index(root, cur->left, &r_index, &h_index_left);
 260                 else {
 261                         cur = cur->right;
 262                         continue;
 263                 }
 264
 265                 if (!prio_tree_right_empty(cur))
 266                         get_index(root, cur->right, &r_index, &h_index_right);
 267                 else {
 268                         cur = cur->left;
 269                         continue;
 270                 }
 271
 272                 /* both h_index_left and h_index_right cannot be 0 */
 273                 if (h_index_left >= h_index_right)
 274                         cur = cur->left;
 275                 else
 276                         cur = cur->right;
 277         }
 278
 279         if (prio_tree_root(cur)) {
 280                 BUG_ON(root->prio_tree_node != cur);
 281                 __INIT_PRIO_TREE_ROOT(root, root->raw);
 282                 return;
 283         }
 284
 285         if (cur->parent->right == cur)
 286                 cur->parent->right = cur->parent;
 287         else
 288                 cur->parent->left = cur->parent;
 289
 290         while (cur != node)
 291                 cur = prio_tree_replace(root, cur->parent, cur);
 292 }
 293
 294 static void iter_walk_down(struct prio_tree_iter *iter)
 295 {
 296         iter->mask >>= 1;
 297         if (iter->mask) {
 298                 if (iter->size_level)
 299                         iter->size_level++;
 300                 return;
 301         }
 302
 303         if (iter->size_level) {
 304                 BUG_ON(!prio_tree_left_empty(iter->cur));
 305                 BUG_ON(!prio_tree_right_empty(iter->cur));
 306                 iter->size_level++;
 307                 iter->mask = ULONG_MAX;
 308         } else {
 309                 iter->size_level = 1;
 310                 iter->mask = 1UL << (BITS_PER_LONG - 1);
 311         }
 312 }
 313
 314 static void iter_walk_up(struct prio_tree_iter *iter)
 315 {
 316         if (iter->mask == ULONG_MAX)
 317                 iter->mask = 1UL;
 318         else if (iter->size_level == 1)
 319                 iter->mask = 1UL;
 320         else
 321                 iter->mask <<= 1;
 322         if (iter->size_level)
 323                 iter->size_level--;
 324         if (!iter->size_level && (iter->value & iter->mask))
 325                 iter->value ^= iter->mask;
 326 }
 327
 328 /*
 329  * Following functions help to enumerate all prio_tree_nodes in the tree that
 330  * overlap with the input interval X [radix_index, heap_index]. The enumeration
 331  * takes O(log n + m) time where 'log n' is the height of the tree (which is
 332  * proportional to # of bits required to represent the maximum heap_index) and
 333  * 'm' is the number of prio_tree_nodes that overlap the interval X.
 334  */
 335
 336 static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
 337                 unsigned long *r_index, unsigned long *h_index)
 338 {
 339         if (prio_tree_left_empty(iter->cur))
 340                 return NULL;
 341
 342         get_index(iter->root, iter->cur->left, r_index, h_index);
 343
 344         if (iter->r_index <= *h_index) {
 345                 iter->cur = iter->cur->left;
 346                 iter_walk_down(iter);
 347                 return iter->cur;
 348         }
 349
 350         return NULL;
 351 }
 352
 353 static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
 354                 unsigned long *r_index, unsigned long *h_index)
 355 {
 356         unsigned long value;
 357
 358         if (prio_tree_right_empty(iter->cur))
 359                 return NULL;
 360
 361         if (iter->size_level)
 362                 value = iter->value;
 363         else
 364                 value = iter->value | iter->mask;
 365
 366         if (iter->h_index < value)
 367                 return NULL;
 368
 369         get_index(iter->root, iter->cur->right, r_index, h_index);
 370
 371         if (iter->r_index <= *h_index) {
 372                 iter->cur = iter->cur->right;
 373                 iter_walk_down(iter);
 374                 return iter->cur;
 375         }
 376
 377         return NULL;
 378 }
 379
 380 static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
 381 {
 382         iter->cur = iter->cur->parent;
 383         iter_walk_up(iter);
 384         return iter->cur;
 385 }
 386
 387 static inline int overlap(struct prio_tree_iter *iter,
 388                 unsigned long r_index, unsigned long h_index)
 389 {
 390         return iter->h_index >= r_index && iter->r_index <= h_index;
 391 }
 392
 393 /*
 394  * prio_tree_first:
 395  *
 396  * Get the first prio_tree_node that overlaps with the interval [radix_index,
 397  * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
 398  * traversal of the tree.
 399  */
 400 static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
 401 {
 402         struct prio_tree_root *root;
 403         unsigned long r_index, h_index;
 404
 405         INIT_PRIO_TREE_ITER(iter);
 406
 407         root = iter->root;
 408         if (prio_tree_empty(root))
 409                 return NULL;
 410
 411         get_index(root, root->prio_tree_node, &r_index, &h_index);
 412
 413         if (iter->r_index > h_index)
 414                 return NULL;
 415
 416         iter->mask = 1UL << (root->index_bits - 1);
 417         iter->cur = root->prio_tree_node;
 418
 419         while (1) {
 420                 if (overlap(iter, r_index, h_index))
 421                         return iter->cur;
 422
 423                 if (prio_tree_left(iter, &r_index, &h_index))
 424                         continue;
 425
 426                 if (prio_tree_right(iter, &r_index, &h_index))
 427                         continue;
 428
 429                 break;
 430         }
 431         return NULL;
 432 }
 433
 434 /*
 435  * prio_tree_next:
 436  *
 437  * Get the next prio_tree_node that overlaps with the input interval in iter
 438  */
 439 struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
 440 {
 441         unsigned long r_index, h_index;
 442
 443         if (iter->cur == NULL)
 444                 return prio_tree_first(iter);
 445
 446 repeat:
 447         while (prio_tree_left(iter, &r_index, &h_index))
 448                 if (overlap(iter, r_index, h_index))
 449                         return iter->cur;
 450
 451         while (!prio_tree_right(iter, &r_index, &h_index)) {
 452                 while (!prio_tree_root(iter->cur) &&
 453                                 iter->cur->parent->right == iter->cur)
 454                         prio_tree_parent(iter);
 455
 456                 if (prio_tree_root(iter->cur))
 457                         return NULL;
 458
 459                 prio_tree_parent(iter);
 460         }
 461
 462         if (overlap(iter, r_index, h_index))
 463                 return iter->cur;
 464
 465         goto repeat;
 466 }